Abstract

Variations in solar irradiance are widely believed to explain
climatic change on 20,000- to 100,000-year time-scales in accordance
with the Milankovitch theory of the ice ages, but there is no
conclusive evidence that variable irradiance can be the cause of abrupt
fluctuations in climate on time-scales as short as 1,000 years. We
propose that such abrupt millennial changes, seen in ice and
sedimentary core records, were produced in part by well characterized,
almost periodic variations in the strength of the global oceanic
tide-raising forces caused by resonances in the periodic motions of the
earth and moon. A well defined 1,800-year tidal cycle is associated
with gradually shifting lunar declination from one episode of maximum
tidal forcing on the centennial time-scale to the next. An amplitude
modulation of this cycle occurs with an average period of about 5,000
years, associated with gradually shifting separation-intervals between
perihelion and syzygy at maxima of the 1,800-year cycle. We propose
that strong tidal forcing causes cooling at the sea surface by
increasing vertical mixing in the oceans. On the millennial time-scale,
this tidal hypothesis is supported by findings, from sedimentary
records of ice-rafting debris, that ocean waters cooled close to the
times predicted for strong tidal forcing.

High resolution ice-core and
deep-sea sediment-core records over the past million years show
evidence of abrupt changes in climate superimposed on slow alternations
of ice-ages and interglacial warm periods. In general these abrupt
changes are spaced irregularly, but a distinct subset of recurring cold
periods, on the millennial time-scale, appears to be almost periodic.
Such events, however, are not clearly apparent in ice-core data after
the termination of the most recent glaciation, about eleven thousand
years (11 kyr) BP (kyr before A.D. 2000). This absence of recent events
has led to the hypothesis that their underlying cause is related to
internal ice-sheet dynamics (ref. 1, p. 35). Interpretations of
sediment-cores by Bond et al. (1, 2) indicate, however, that
a 1- to 2-kyr periodicity persisted almost to the present,
characterized by distinct cooling events, including the Little Ice Age
that climaxed near A.D. 1600. Although evidence that cooling was more
intense during glacial times may be explained by some aspect of
ice-dynamics, a continuation of cooling events throughout the
postglacial Holocene era suggests an alternative underlying mechanism.

The 1- to 2-kyr Ice-Rafted Debris (IRD) Cycle.

In a comprehensive comparison of ice-core and sediment-core data, Bond
et al. (1) found persistent episodic cooling events recorded
as increases in the amounts of IRD in deep sea sediments of the North
Atlantic Ocean basin over the past 80 kyr. Consistent periodicity was
demonstrated by averaging the times between inferred cool events over
12-kyr time intervals. This “pacing” of events was found to be
restricted to a narrow range between 1,328 and 1,795 years, with a
grand average of 1,476 ± 585 yr, that they termed a “1–2 kyr
climate cycle.”

Similar to these oceanic cooling events, but less frequent and regular,
are Dansgaard/Oeschger events seen in
18O/16O data of glacial
ice. Although sudden warming events are more conspicuous, these data
also show cooling events. Bond et al. (1) found that
Dansgaard/Oeschger cooling events coincide with nearly every IRD
event during Stage 3 of the last glaciation when Dansgaard/Oeschger
events were best developed (ref. 1, p. 51). They also found that
Heinrich events, massive discharges of icebergs at intervals of 6–9
kyr in the North Atlantic Ocean, were in most cases preceded by IRD
events by 0.5 and 1 kyr (ref. 1, p. 48), suggesting a close link
between the two phenomena.

Bond et al. (1) proposed “that the millennial scale
climate variability documented in Greenland ice cores and North
Atlantic sediments through the last glaciation was not forced by ice
sheet instabilities, but instead arose through modulation of a
pervasive 1–2 kyr cycle. The persistence of the cycle through
virtually the entire 80 kyr record points to a single forcing mechanism
that operated independently of the glacial-interglacial climate
states” (ref. 1, p. 55). They did not, however, propose a specific
mechanism.

The IRD events identified by Bond et al. (1, 2) show high
spectral power density in a broad band centered at about 1,800 years
(0.55 ± 0.15 cycles/kyr). The authors do not explain why this
period is so much larger than the 1,476-year average pacing of cool
events, but the time-distribution of pacing (ref. 1, Fig.
6c; G. Bond, private communication) suggests that a majority
of the events were about 2,000 years apart, with occasional additional
events occurring about half-way between, evidently too infrequent to
cancel out a dominant spectral peak near 1,800 years. Bond et
al. (2) in addition found a spectral peak near 5,000 years whose
possible cause was also not explained. We now propose an oceanic tidal
mechanism that may explain the basis for both of these spectral peaks,
consistent with the actual times of IRD events.

A Proposed Tidal Mechanism for Periodic Oceanic Cooling.

In a previous study (3) we proposed a tidal mechanism to explain
approximately 6- and 9-year oscillations in global surface temperature,
discernable in meteorological and oceanographic observations. We first
briefly restate this mechanism. The reader is referred to our earlier
presentation for more details. We then invoke this mechanism in an
attempt to explain millennial variations in temperature.

We propose that variations in the strength of oceanic tides cause
periodic cooling of surface ocean water by modulating the intensity of
vertical mixing that brings to the surface colder water from below. The
tides provide more than half of the total power for vertical mixing,
3.5 terawatts (4), compared with about 2.0 terawatts from wind drag
(3), making this hypothesis plausible. Moreover, the tidal mixing
process is strongly nonlinear, so that vertical mixing caused by tidal
forcing must vary in intensity interannually even though the annual
rate of power generation is constant (3). As a consequence,
periodicities in strong forcing, that we will now characterize by
identifying the peak forcing events of sequences of strong tides, may
so strongly modulate vertical mixing and sea-surface temperature as to
explain cyclical cooling even on the millennial time-scale.

As a measure of the global tide raising forces (ref. 5, p. 201.33), we
adopt the angular velocity, γ, of the moon with respect to perigee,
in degrees of arc per day, computed from the known motions of the sun,
moon, and earth. This angular velocity, for strong tidal events, from
A.D. 1,600 to 2,140, is listed in a treatise by Wood (ref. 5, Table
16). We extended the calculation of γ back to the glacial age by a
multiple regression analysis that related Wood's values to four
factors that determine the timing of strong tides: the periods of the
three lunar months (the synodic, the anomalistic, and the nodical), and
the anomalistic year, defined below. Our computations of γ first
assume that all four of these periods are invariant, with values
appropriate to the present epoch, as shown in Table
1. We later address secular variations.
Although the assumption of invariance is a simplification of the true
motions of the earth and moon, we have verified that this method of
computing γ (see Table 2) produces
values nearly identical to those listed by Wood, the most serious
shortcoming being occasional shifts of 9 or 18 years in peak values of
γ.

A time-series plot of Wood's values of γ (Fig.
1) reveals a complex cyclic pattern. On
the decadal time-scale the most important periodicity is the Saros
cycle, seen as sequences of events, spaced 18.03 years apart. Prominent
sequences are made obvious in the plot by connected line-segments that
form a series of overlapping arcs. The maxima, labeled A, B, C, D, of
the most prominent sequences, all at full moon, are spaced about 180
years apart. The maxima, labeled a, b, c, of the next most prominent
sequences, all at new moon, are also spaced about 180 years apart. The
two sets of maxima together produce strong tidal forcing at
approximately 90-year intervals.

Varying strength in an estimate of the tide raising forces, derived
from Wood (ref. 5, Table 16). Each event, shown by a vertical line,
gives a measure of the forcing in terms of the angular velocity of the
moon, γ, in arc degrees per day, at the time of the event. Arcs
connect events of strong 18.03-year tidal sequences. Centennial maxima
are labeled, with the final one, “D”, occurring in A.D. 2151.

As an indication that tidal forcing might influence temperature,
Keeling and Whorf (3) found that times of cool surface temperature, on
pentadal to decadal time-scales, tended to occur at 9-year intervals
near events b and C of Fig. 1: thus, at times of strong 18.03-year
Saros cycle tidal events. They occurred, however, at 6-year intervals
midway between events b and C, when the Saros cycle events were weak
and 6-year tidal forcing was more prominent than 9-year forcing. They
also noted a general tendency for interdecadal warming near 1930, when
Saros cycle forcing was weak, and a lack of warming when this forcing
was strong near 1880 and 1970, as though cooling near times of strong
forcing lingered for several decades, despite the identified events
being only single tides.

The 1,800-Year Tidal Cycle.

When the time-interval of computed strong global tidal forcing is
extended to include all events from 500 B.C. to A.D. 4000 (Fig.
2), two longer periodicities become
evident, defined by extensions of the maxima, labeled A–D and a–c, as
in Fig. 1. First, near the beginning and end of the 4,000 years
plotted, every second 180-year maximum is stronger, producing a
periodicity of about 360 years. More striking is a well defined
millennial cycle with maxima at 398 B.C., A.D. 1425, and A.D. 3107. The
latter maximum is almost matched in strength, however, by one in A.D.
3452 such that a lesser intermediate event in A.D. 3248 appears to
define the repeat period of the cycle as 1,823 years. The actual
maximum in A.D. 3107, however, would define an interval of only 1,682
years.

Extension of Fig. 1 to illustrate millennial periodicity in tide
raising forces since 500 B.C. The angular velocity, γ, was computed
from functions listed in Table 2. Events of a 180-year cycle, all at
full moon, are labeled with times of occurrence (B.C. or A.D.). The
1,800-year cycle is evident as a progression of solar-lunar declination
difference, listed at the top of the figure in degrees of arc of the
moon above (or below) the ecliptic.

The existence of tidal forcing at intervals of about 1,800 years was
proposed by Otto Petersson in 1914 and 1930 [cited by Lamb (ref. 6, p.
220)]. Cartwright (7) identified events similar to those plotted in
Fig. 2, consisting of strong tidal forcing 93 years apart from A.D.
1340 to 1619 and again from 3182 to 3461: thus, an average interval
between clusters of 1,842 years. Keeling and Whorf (3) briefly
discussed the astronomical basis for an 1,800-year tidal cycle.
Computations of γ over many millennia show this 1,800-year cycle and
demonstrate that the spacing of maximum events is irregular. As we will
show next, the cycle is well defined, however, with an exact average
period when computed for the present epoch.

The greatest possible astronomical tide raising forces would occur if
the moon and the sun were to come into exact mutual alignment with the
earth at their closest respective distances (7). If we only consider
motions as they exist today (the present epoch) we can determine
departures from this reference event as simple functions of the
separation-intervals between four orbital conditions that determine
these alignments and distances. The most critical condition is
closeness in time to syzygy, a term that refers to either new moon or
full moon. The return period of either lunar phase defines the 29.5-day
synodic month. Maxima in tidal strength occur at both new and full
moon: i.e., “fortnightly.”

The next most critical condition of tidal forcing is the closeness of
the moon to perigee, the point of the moon's elliptical orbit closest
to the earth. The fortnightly tides vary in strength as a function of
the time-separation of perigee and syzygy. The moon is at perigee on
average once every 27.6-day anomalistic month. When it is close to both
perigee and syzygy, perigean tides occur. For each moon, new or full,
this happens on average every 411.78 days, the beat period of the
synodic and anomalistic months.

A third important condition is the closeness of the moon to a node,
either of two points in its orbit that lie on the ecliptic, the plane
of the earth's orbit around the sun. The moon crosses the ecliptic
twice every 27.2-day nodical month. Maxima in perigean tides occur when
the moon is close to the ecliptic, as well as to perigee and syzygy.
This happens, on average, every 2.99847 calendar years to create the
perigean eclipse cycle, equal to twice the beat period of the nodical
and anomalistic months. The 6-year and 9-year tidal events that tend to
correlate with times of cool global temperatures (3) are synchronous
with every second or third perigean eclipse cycle, respectively.

A fourth condition necessary for determining maximal tidal forcing is
the closeness of the earth to perihelion, the point on the earth's
elliptical orbit closest to the sun, occupied every anomalistic year of
365.2596 days. When an analysis is made to find the times when all four
conditions are most closely met, the 1,800-year cycle becomes apparent
as a slow progression of solar-lunar declinational differences that
coincide with progressive weakening and then strengthening of
successive centennial maxima in tidal forcing (Fig. 2). The 1,800-year
cycle thus represents the time for the recurrence of perigean eclipses
closely matched to the time of perihelion. Progressively less close
matching of perigee, node, and perihelion with syzygy occur, on
average, at intervals of 360, 180, 90, 18, and 9 years.

The long term average period of the 1,800-year cycle can be computed
from the circumstance that the period of the perigean eclipse cycle
falls 0.610061 days short of 3 anomalistic years. Independent of the
condition of syzygy, the long term period is 1795.26 years
(2.99847 × 365.2596/0.610061), equal to the beat period of the
anomalistic year with one-third of the period of the perigean eclipse
cycle. The actual timing of specific maximum events of the 1,800-year
cycle depends, however, also on the timing of syzygy. This additional
requirement causes the intervals between specific maxima to occur at
intervals of 1,682, 1,823, or 2,045 years, or even occasionally ±
18.03 years from these three principal intervals. (An example is the
1,682-year interval from A.D. 1425 to 3107, noted above.) The maxima of
the centennial cycles are also irregular. The 360-year cycle has
principal intervals of 345, 363, and 407 years, plus occasionally
others. The 180-year cycle has a wide range of intervals, in 9-year
increments, from 141 to 204 years. The 90-year tidal interval can be
either 84 or 93 years.

A 5,000-Year Modulation of the 1,800-Year Cycle.

A further millennial cycle arises from variability in the strengths of
the maxima of the 1,800-year cycle. In the lowest plot of Fig.
3 is shown a hypothetical sequence of
tidal events assuming, as a starting point, zero separation-intervals
of syzygy from perigee, lunar node, and perihelion. The calculations
assume that the lunar months and anomalistic year have constant periods
appropriate to the present epoch. The γ value of all tidal events
above a threshold of 17.150° per day are plotted. Every second or
third 1,800-year maximum in γ is seen to be more prominent. The cause
of this pattern can be understood by viewing the top plot of Fig. 3,
which shows the separation-interval of syzygy from perihelion, in days,
for all tidal events in the 360-year centennial cycle. This
time-difference describes a pattern consisting of a generally declining
difference interrupted by an abrupt upward shift that occurs 61 times
in a simulation of 283,674 kyr (not all plotted): hence, an average
period of 4,650 years.

Varying strength of the global tide raising forces (bottom plot), as in
Figs. 1 and 2, together with parameters (top and middle plots) that
reveal the basis for the 1,800- and 5,000-year tidal cycles, as
described in the text. The plots are for a hypothetical 110-kyr
sequence of tidal events beginning with the moon, sun, and earth in
perfect alignment and closest approach (zero separation-intervals),
producing a maximum γ of 17.165° per day never again attained.
Tidal events occurring near peaks in the 5,000-year cycle (near zero
crossings of top plot) are connected by straight lines to reveal their
pattern (which includes a 23-kyr cycle not discussed in the text).

Shown in the middle plot of Fig. 3 is the departure, in arc degrees, of
the moon from the plane of the ecliptic for the same events as shown in
the upper plot. This angular difference describes a similar pattern to
that of the upper plot, but with the average period of the 1,800-year
cycle. The separation-interval of syzygy from perigee (not shown)
remains small (less than 2 hr) for all of the maximum millennial events
shown in Fig. 3. Thus, the 1,800-year cycle arises from progressive
mismatches of syzygy and lunar node, the 4,650-year cycle from
progressive mismatches of syzygy and perihelion. These two cycles are
incommensurate even though both are expressed by recurring maxima of
the 1,800-year cycle.

Observational Tests of Millennial Tidal Climatic Forcing.

Time-series of ice-rafted debris (IRD) from sedimentary cores in the
North Atlantic ocean (1, 2), and associated temperature proxy data,
show evidence of repeated rapid cooling events in the Northern
Hemisphere, as summarized in “The 1- to 2-kyr IRD Cycle” section
above. We now show, from results of both spectral analysis and direct
comparisons of events, that strong oceanic tidal forcing may have
occurred in association with IRD events.

Spectral analysis of the IRD records, from 1- to 31-kyr BP, reproduced
in Fig. 4 from Bond et al.
(2), show broad peaks centered at 1,800 and 4,670 years (Fig.
4A), in contrast to an average pacing between IRD events of
1,470 ± 532 years. The peak periods agree closely with the
1,800-year and 5,000-year tidal cycle periods, shown by added vertical
red lines. Bond et al. (2) also determined the phasing of
the 1,800-year IRD band by filtering their data with a bandpass
centered at 1,800 years (Fig. 4B). Cold periods, indicated
by high filter values, nearly coincide with 1,800-year tidal events,
shown by added horizontal red lines.

Multitaper spectral analysis of glacial-Holocene petrologic events from
cores VM 29–191 and VM 23–81 (reproduced from ref. 2, Fig. 7),
compared with periodicities in tidal forcing. Overlain in red are the
averages (calculated from 0 to 31.1 kyr BP) of the 1,800- and
5,000-year tidal periods (A) and times of peak forcing
of the former cycle (B). Tidal timing and periodicity
assume invariant orbital parameters, except for the 5,800-year period
that is based on assuming secular variability of climatic precession,
as described in the “Secular Variations in Tidal Forcing” section
of the text.

A possible explanation for the disparity between the pacing of about
1,500 years, and the spectral period of about 1,800 years in the IRD
data, is provided in Fig. 5 by a direct
comparison of IRD cold events (dashed black lines) with times of strong
tidal forcing (solid red lines). Between 0.6 and 31.2 kyr BP, 18 IRD
events collectively exhibit an average spacing of 1,800 years while 4
others (“7”, “YD,” and one each near 14 kyr BP and 1.4 kyr
BP) are spaced nearly midway between events of the first subset, 3 of
these in a cluster near 12 kyr BP. The resulting bimodal pacing
accounts for finding a broad spectral peak near 1,800 years, despite an
average pacing of 1,470 years. Furthermore, the 1,800-year spectral
peak is again found when the IRD record is extended back to 80 kyr BP
(ref. 1, Fig. 8), with similar phasing of the associated bandpass.
Additional clusters of events with about half the pacing of the
majority again suggests a bimodal distribution in pacing (Fig. 6 in
ref. 1).

Glacial-Holocene deep-sea core record of ice-rafted debris, petrology,
and isotopes of the North Atlantic Ocean basin (from ref. 2, Fig. 6; BP
in kyr before A.D. 1950), which shows evidence of pervasive
millennial-scale fluctuations in climate. Overlaid in red are times of
peak forcing in the 1,800-year tidal cycle.

A possible cause of an 1,800-year IRD cycle, consistent with tidal
forcing, is the concept of “threshold behavior” of nonlinear
systems suggested by Bond et al. (ref. 1, p. 51). Suppose
that the primary mechanism of the 1- to 2-kyr IRD cycle is an unstable
system in which distinct periodic forcing is always capable of causing
a threshold to be exceeded, but that the threshold is occasionally
exceeded without this forcing operating. The result could be an
irregular pacing of events without obliterating the evidence of a
cyclic process associated with this forcing.

A handicap in establishing a cyclic character to sedimentary core data
is the uncertainty in their time-scale. Records of IRD events from four
separate sedimentary cores in the North Atlantic, plotted together by
Bond et al. (ref. 1, Fig. 14) show deviations in the timing
of IRD events, from one core to another, of the same order as their
deviations from the times of 1,800-year tidal events. For the Holocene
era, a more precise comparison of cooling and tidal events is afforded
by dust layers in sediments of Elk Lake, situated near the boundary of
forest and prairie in north-central United States (8). The layers,
millimeter-scale annual laminations that permit high resolution
calibration of climatic events (± 200 years) back to 10 kyr BP, are
believed to represent cold, dry periods in a region sensitive to
climate change (8).

The three most prominent dust layers of Elk Lake (Fig.
6) are nearly coincident with 1,800-year
tidal events at 4,239, 5,921, and 7,744 yr BP. Suggestive of a
world-wide phenomenon, the most recent Elk Lake event, dated at 4,100
yr BP, is essentially contemporaneous with a dust spike in Peruvian
Ice, dated at 4,200 ± 200 yr BP, marking a major drought in the
Amazon Basin, and a dust layer, dated at 4,000 ± 100 yr BP in
sediments of the Red Sea, that may have been caused by widespread
drought, contributing to the collapse of Akkadia, the world's first
empire (9).

Profile of mass accumulation rate of aluminum (AL-MAR in
mg/cm2/yr) in sediments of Elk Lake, Minnesota [from
Dean (ref. 8, Fig. 2)]. Overlain in red are the times of peak forcing
in the 1,800-year tidal cycle (at 4,239, 5,921, and 7,744 yr BP).

We summarize the relationship of strong global tidal forcing to times
of inferred cooling events in Fig. 7. The
timing of dust layers, from lake sediments, and of the Little Ice Age,
from historic data, correspond closely with peaks of the 1,800-year
tidal cycle. If four previously identified exceptional events (dashed
vertical lines) are excluded, the timing of the remaining IRD events
also corresponds to peak tidal events almost within the stated
uncertainty in their dating, not less than 5% (ref. 1, p. 39). The IRD
event (number 5) near 8,100 yr BP is particularly noteworthy because it
appears to be associated with the most abrupt and widespread climate
shift known from the past 10 kyr (10); it is believed to have been
initiated by a large freshwater pulse from Laurentide lakes, dated at
8,470 yr BP, that reduced surface ocean salinity in the North Atlantic
Ocean, thereby causing widespread cooling near 8,200 yr BP (11). Two
recently drilled sedimentary cores show multiple IRD events between
8,300 and 7,400 yr BP (ref. 1, Fig. 14). Together with the Elk Lake
dust layer of 7,800 yr BP, these data suggest prolonged or repeated
cooling well beyond the time expected for a freshwater discharge to
directly affect climate. The maximum tidal forcing near these events at
7,744 yr BP was the greatest in 20,000 years, preceded and succeeded by
strong forcing at 8,089 and 7,381 yr BP of the 360-yr tidal cycle. Thus
the tidal hypothesis suggests that cooling initiated by a freshwater
pulse may have been prolonged by tidal forcing. Also consistent with
tidal forcing is the possibility that the timing of the freshwater
pulse occurred during a warm phase of the 1,800-year tidal cycle, about
700 years before maximum forcing at 7,744 yr BP.

Comparison of late-glacial and Holocene sedimentary core chronology of
the North Atlantic Ocean basin with the times of tidal forcing. Tidal
events are shown as in Figs. 1 and 2 with times of 1,800-year climactic
events (in kyr BP) listed below. These climactic events are connected
by line segments. Those that contribute to the 5,000-year tidal cycle
are marked with asterisks. Immediately above this plot are vertical
lines indicating cool periods inferred from the deep-sea core records,
labeled as in Fig. 5. Their timing is derived from Fig. 5, except for
Event 1 and Events 3–8, which are dates quoted in the text of ref. 2,
and Event 2, inferred from Bond et al. (ref. 1, Fig.
14). Plotted as arrows are the times of dust layers in Elk Lake,
Minnesota, the beginning of the Akkadian drought [as reported by Kerr
(9)], the Little Ice Age, and the end of the Younger Dryas (YD) [Bond
et al. (2)]. Events consistent with the hypothesis of
tidal forcing of climate are shown as solid lines, exceptions as dashed
lines.

Secular Variations in Tidal Forcing.

Over tens of millennia it is unrealistic to assume that the periods of
the lunar months and the anomalistic year are constant, as we have in
our calculations described so far. We have no information to determine
secular variations in the lunar months, but we have recalculated γ,
our measure of tidal forcing, taking account of secular variations in
the time of passage of perihelion and in the eccentricity of the
earth's orbit as listed in a table kindly supplied to us by A. Berger
(private communication).

Variations in the anomalistic year are proportional to
P/(P − 1) where P denotes the
period of “climatic precession,” defined as the time-interval
between two consecutive passages of the vernal equinoxial point at
perihelion. The period of climatic precession has been estimated (12)
to have varied between 19 and 28 kyr during the past 60 kyr, with the
largest variations before 33 kyr BP.

When a variable anomalistic year, derived from the prescribed secular
variation of P , is introduced into our calculations, the
average period of the 1,800-year cycle, from 33 kyr BP to the present,
is only slightly altered from 1,795 to 1,805 years. The 5,000-year
modulation of this cycle is significantly lengthened, from 4,787 to
5,769 years, but is still consistent with the corresponding spectral
band for IRD events (shown in Fig. 4). The magnitudes of peak tidal
events of the 1,800-year cycle are almost identical back to 10 kyr BP,
and the dates are identical back to 14 kyr BP. Thus our conclusions
with respect to climate forcing of the Holocene should not be affected
by our neglect of secular orbital variations.

Before the Holocene era the timing of peak tidal events gradually
departs from that calculated, assuming a constant anomalistic year such
that the 1,800-year peak occurred 123 years earlier at 33,066 yr BP,
still an insignificant difference when making comparisons with events
seen in core records. Variability in magnitude of the peak 5,000-year
events diminishes between 16 and 33 kyr BP, during a time of rapidly
changing climatic precession, suggesting that the assumption of a
constant anomalistic year exaggerates variability in γ on long
time-scales.

Moreover, we have noticed a similar tendency on the decadal time-scale.
The plotted arcs of the 18.03-year Saros cycles, shown in Fig. 1, based
on accurate orbital data, are more regular than those plotted in Fig.
2, based on assuming constant lunar months. The irregularities that we
find in tidal strength and timing over longer periods might further
decrease if we prescribed more exact motions of the moon and earth, as
well as prescribing variable climatic precession.

[A cause for such greater regularity in tidal forcing might be
resonances of other bodies of the solar system, especially the outer
planets. We are struck by the close correspondence of the average
period of the 180-year tidal cycle of 179.5 years (1/10 of that of
the 1,800-year cycle) and the period of the sun's rotation about the
center of mass of the solar system of 179.2 years, the latter a
manifestation of planetary resonances (13).]

We have also calculated the effect on γ of varying eccentricity.
First, we estimated the variation of γ with distance, R ,
of the earth from the sun by establishing the average seasonal cycle of
γ derivable from the data of Wood (ref. 5, Table 16). We then assumed
a dependence proportional to R3 for
both the seasonal and secular rate of change in R. The
1,800-year cycle in γ remains almost exactly as at constant
eccentricity, but a 100-kyr variation is introduced into γ that is
several times as large as the amplitude of the 1,800-year cycle. We
tentatively conclude that, although varying eccentricity strongly
affects tidal forcing, and could possibly contribute to the 100-kyr
cycle of glaciation, it has little influence on the cycles under
discussion here.

Ramifications of the Tidal Hypothesis.

The details of the tidal hypothesis are complex. There is much about
tidal forcing that we do not know, and there is not space here to
discuss all that we do know that could contribute to proving whether it
is the underlying cause of some, or all, of the events of rapid climate
change. We are convinced, however, that, if the hypothesis is to a
considerable degree valid, the consequences to our understanding of the
ice-ages, and of possible future climates, are far from trivial.

Should the tidal hypothesis of quasi-periodic cooling of the oceans
turn out to be correct, a prevailing view that the earth's postglacial
climate responds mainly to random and unpredictable processes would be
modified or abandoned. The 1,800-year tidal cycle would be recognized
as a principal driver of climate change in the Holocene, causing shifts
in climate more prominent and extensive than hitherto realized. The
Little Ice Age would be seen to be only a lesser cooling episode in a
series of such episodes. Viewed today as of “possibly global
significance” (14), it would probably be confirmed as such, being
linked to global tidal forcing. Other major climatic events since the
glacial period, such as drought near the time of collapse of the
Akkadian empire, might also be found to be linked to a global process.

Looking ahead, a prediction of “pronounced global warming” over
the next few decades by Broecker (15), presumed to be triggered by the
warm phase of an 80-year climatic cycle of unidentified origin, would
be reinterpreted as the continuation of natural warming in roughly
centennial increments that began at the end of the Little Ice Age, and
will continue in spurts for several hundred years. Even without further
warming brought about by increasing concentrations of greenhouse gases,
this natural warming at its greatest intensity would be expected to
exceed any that has occurred since the first millennium of the
Christian era, as the 1,800-year tidal cycle progresses from climactic
cooling during the 15th century to the next such episode in the 32nd
century.

Acknowledgments

We thank Gerard Bond for numerous helpful discussions and
André Berger for advice on the astronomical tides and valuable
astronomical data. We also thank David Cartwright, Christopher Charles,
Walter Dean, Devandra Lal, Walter Munk, and Jeff Severinghaus for
advice on climate change and tidal theory. We are especially indebted
to Fergus Wood for pointing out to us that the function γ would serve
to indicate the strength of tidal forcing. We owe much to his having
tabulated γ over more than 500 years. It was the curious progressive
increase in γ from Event D to Event A of Fig. 1, suggestive of a
millennial periodicity, that led us to discover the 1,800-year tidal
cycle. Financial support was provided by the National Science
Foundation (Grant ATM-97-11882) and the U.S. Department of Energy
(Grant FG03-95ER-62075).

Footnotes

↵* To whom reprint requests should be addressed. Email:
cdkeeling{at}ucsd.edu.